AGGRCOW - Aggressive cows


Farmer John has built a new long barn, with N (2 <= N <= 100,000) stalls. The stalls are located along a straight line at positions x1,...,xN (0 <= xi <= 1,000,000,000).

His C (2 <= C <= N) cows don't like this barn layout and become aggressive towards each other once put into a stall. To prevent the cows from hurting each other, FJ wants to assign the cows to the stalls, such that the minimum distance between any two of them is as large as possible. What is the largest minimum distance?

Input

t – the number of test cases, then t test cases follows.
* Line 1: Two space-separated integers: N and C
* Lines 2..N+1: Line i+1 contains an integer stall location, xi

Output

For each test case output one integer: the largest minimum distance.

Example

Input:

1
5 3
1
2
8
4
9

Output:

3

Output details:

FJ can put his 3 cows in the stalls at positions 1, 4 and 8,
resulting in a minimum distance of 3.


hide comments
sameerchour: 2020-04-26 19:27:18

Guys , for those who think for largest minimum distance , it should be 1,4,9 , not 1,4,8. Actually , it does not make any difference, because , minimum dist between two cows is (4-1) = 3 , not (9-5) = 4 , 4 is not the minimum distance, so we have to output the largest minimum distance we could get , like (1-2), (4-1), we could place cow at 1,8,9 , (8-1) = 7, but then , minimum distance would be (9-8) = 1 , I hope you understand , because the wordings are very confusing and I was stuck for a long time !! hope this helps !!

az_09_18je0028: 2020-04-19 09:37:27

AC in one go::)

sudhanshu751: 2020-04-05 08:12:07

For everyone that is stuck/not able to think of the logic, check out the TopCoder tutorial for Binary Search [discrete binary search] .

After learning from that tutorial and spending some more time on problem you will be able to solve.

blackhat_130: 2020-03-19 20:51:11

You should think of doing binary search on difference.
Topcoder tutorial on binary search might be useful.

prabhudeen: 2020-03-17 20:00:38

nice question on binary search and gready approch takes time to come up the right solution.

arun m dabbe: 2020-02-15 08:43:29

Very interesting problem , classic .

sayan_244: 2020-01-30 15:46:11

>.> You need to be bit lucky for the greedy approach to strike. Took me a whole day.

And rare for me but AC in a single go :p
P.S :-Read Topcoder as suggested by many. Its not just greedy alone but coupled with Binary Search

Last edit: 2020-01-30 15:50:43
abhi1999: 2020-01-23 15:20:28

Where can i find solution of the problem

transonviet: 2020-01-02 05:32:50

AC in one go

heromayank2: 2019-12-24 15:20:19

Poor Explanation


Added by:Roman Sol
Date:2005-02-16
Time limit:2s
Source limit:10000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:USACO February 2005 Gold Division